Simplify (x^2+20x+100)/(x^2-100)

$\frac{x^{2} + 20 x + 100}{x^{2} - 100}$

Step 1

Factor using the perfect square rule.

Rewrite $100$ as $10^{2}$ .

$\frac{x^{2} + 20 x + 10^{2}}{x^{2} - 100}$

Check that the middle term is two times the product of the numbers being squared in the first term and third term.

$20 x = 2 \cdot x \cdot 10$

Rewrite the polynomial.

$\frac{x^{2} + 2 \cdot x \cdot 10 + 10^{2}}{x^{2} - 100}$

Factor using the perfect square trinomial rule $a^{2} + 2 a b + b^{2} = {(a + b)}^{2}$ , where $a = x$ and $b = 10$ .

$\frac{{(x + 10)}^{2}}{x^{2} - 100}$

Step 2

Simplify the denominator.

Rewrite $100$ as $10^{2}$ .

$\frac{{(x + 10)}^{2}}{x^{2} - 10^{2}}$

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = x$ and $b = 10$ .

$\frac{{(x + 10)}^{2}}{(x + 10) (x - 10)}$

Step 3

Cancel the common factor of ${(x + 10)}^{2}$ and $x + 10$ .

Factor $x + 10$ out of ${(x + 10)}^{2}$ .

$\frac{(x + 10) (x + 10)}{(x + 10) (x - 10)}$

Cancel the common factors.

Cancel the common factor.

$\frac{(x + 10) (x + 10)}{(x + 10) (x - 10)}$

Rewrite the expression.

$\frac{x + 10}{x - 10}$